Factorization

Factorization is the most foundational topic in algebra. Every Quadratic Equation requires factorization in it. Today I am going to show you how to factorize and the deadly error most people do when factorizing. Consider the linear equation

2acx – 6acy
To factorize all you have to do is take out all the common terms existing in both terms (at the same time) and bracket the remainder of the sum.

2ac(x – 3y)………………that’s the final answer.

Consider the equation……6qp^2 +12pq^2

What are the common terms? 6 occurs in both, only one q occurs in both and only one p occurs in both. Hence the factors are 6,p and q.

6pq(p + 2q)………………..that’s the final answer.

Consider the equation………bc^3 – b^2c^2
what are the common terms? b occurs in both and not c, but c^2 occurs in both. Hence the common factors are b and c^2. You must take out the greatest factor occurring in the terms of the Equation.

bc^2( c – b)………………….that’s the final answer.

That’s about it when factorizing, now I am going to tell you what error to avoid. Consider the equation…….2x^2 – 16x = 0

…………………2x^2 – 16x = 0

divide by 2……... x^2 – 8x = 0
divide by x……… x – 8 = 0

solve for x……….x = 8

This is the biggest error you can make in factorizing. Did you notice my error? Did you notice it was a quadratic equation? If you did realize, where are my 2 solutions for x???

This is the correct and only way to solve the same equation above.

………………2x^2 – 16x = 0

Factorizing…… 2x(x – 8) = 0

Solve for x……. x = 0 and x = 8


Never divide an equation by a letter term, you can only divide by a number term provided only and only if the equation is equal to zero. Never in any point in time divide by x. You will lose a term x = 0

In the S.A.T the exam does not give you factorizing questions, instead they give you questions that involve a little factorizing such as solve for x in the equation…….x^2 + 5x – 6 = 0

This concludes factorization, I hope my viewers understand every step!